Minesweeper thermodynamics
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Minesweeper thermodynamics
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Re: Minesweeper thermodynamics
#2now this is time well spent
Re: Minesweeper thermodynamics
#3Only tangentially related, but Dragonsweeper is an interesting extension of minesweeper where you have hit points and the "mines" have attack values. I got a better appreciation for the mechanics of minesweeper by playing it; it's surprisingly deep. https://danielben.itch.io/dragonsweeper
Re: Minesweeper thermodynamics
#4I hacked up a version of minesweeper that was “forgiving:” if there was no selection that was provably safe, it gave you a safe move. If you picked any square that was not provably a bomb, it would not be a bomb.
Typically, as long as you don’t select a number of bombs equal to the number of squares , your first move is safe. I just extended that for the whole game.
If you select N-1 bombs, you always win on the first move..
Re: Minesweeper thermodynamics
#5The article discusses Boltzmann's formula exp(-E/kT). I was recently looking at the same formula in the context of semiconductors and I realized that Boltzmann's constant k is only needed because temperature uses bad units. If we measured temperature in energy instead of degrees, then Boltzmann's constant drops out. For instance, you could express room temperature as 25 meV (milli electron volts) or 2444 joules/mole and the constant disappears. Likewise, the constant in the ideal gas law disappears if you measure temperature as energy rather than degrees Kelvin. In other words, degrees Kelvin is a made-up unit that should be abandoned. (I'm not sure I believe this, but I don't see a flaw.)
Re: Minesweeper thermodynamics
#6I hacked up a version of minesweeper that was “forgiving:” if there was no selection that was provably safe, it gave you a safe move. If you picked any square that was not provably a bomb, it would not be a bomb. Typically, as long as you don’t select a number of bombs equal to the number of squares , your first move is safe. I just extended that for the whole game. If you select N-1 bombs, you always win on the firs…
Ha! This is NP-Complete, no? In practice, it probably doesn't matter but my bet is that there are some configurations that will take exponential time to see if the player should be "forgiven".
Re: Minesweeper thermodynamics
#7[deleted]
Re: Minesweeper thermodynamics
#8I hacked up a version of minesweeper that was “forgiving:” if there was no selection that was provably safe, it gave you a safe move. If you picked any square that was not provably a bomb, it would not be a bomb. Typically, as long as you don’t select a number of bombs equal to the number of squares , your first move is safe. I just extended that for the whole game. If you select N-1 bombs, you always win on the firs…
Ha! This is NP-Complete, no? In practice, it probably doesn't matter but my bet is that there are some configurations that will take exponential time to see if the player should be "forgiven".
I made winsweeper, which will move the mine if there is no safe tile left for you to discover.
Re: Minesweeper thermodynamics
#9The article discusses Boltzmann's formula exp(-E/kT). I was recently looking at the same formula in the context of semiconductors and I realized that Boltzmann's constant k is only needed because temperature uses bad units. If we measured temperature in energy instead of degrees, then Boltzmann's constant drops out. For instance, you could express room temperature as 25 meV (milli electron volts) or 2444 joules/mole…
Yes! Units are up to you (with some constraints)! Physicists do this in practice a lot: https://en.wikipedia.org/wiki/Natural_units
Re: Minesweeper thermodynamics
#10I hacked up a version of minesweeper that was “forgiving:” if there was no selection that was provably safe, it gave you a safe move. If you picked any square that was not provably a bomb, it would not be a bomb. Typically, as long as you don’t select a number of bombs equal to the number of squares , your first move is safe. I just extended that for the whole game. If you select N-1 bombs, you always win on the firs…
Ha! This is NP-Complete, no? In practice, it probably doesn't matter but my bet is that there are some configurations that will take exponential time to see if the player should be "forgiven".
Yeah I've debugged another game that attempted this and this system resulted in the game lagging as hard sometimes.